# load "Ask a A Manager 2021 Survey" googlesheet
# https://www.askamanager.org/
ask_a_manager_2021 <- read_csv(here::here("data","ask_a_manager.csv"))

skimr::skim(ask_a_manager_2021)

Data summary
Name	ask_a_manager_2021
Number of rows	26765
Number of columns	18
_______________________
Column type frequency:
character	14
logical	2
numeric	1
POSIXct	1
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	n_unique
how_old_are_you	0	1.00	5	10	7
industry	62	1.00	2	171	1084
job_title	0	1.00	1	126	12838
additional_context_on_job_title	19868	0.26	1	781	6612
currency	0	1.00	3	7	11
additional_context_on_income	23851	0.11	1	1143	2839
country	0	1.00	1	209	297
state	4761	0.82	4	114	125
city	23	1.00	1	171	4070
overall_years_of_professional_experience	0	1.00	9	16	8
years_of_experience_in_field	0	1.00	9	16	8
highest_level_of_education_completed	202	0.99	3	34	6
gender	155	0.99	3	29	5
race	151	0.99	5	125	47

Variable type: logical

skim_variable	n_missing	complete_rate	mean	count
other_monetary_comp	26765	0	NaN	:
currency_other	26765	0	NaN	:

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
annual_salary	0	1	144988	5488158	0	54000	75712	110000	8.7e+08	▇▁▁▁▁

Variable type: POSIXct

skim_variable	n_missing	complete_rate	min	max	median	n_unique
timestamp	0	1	2021-04-27 11:02:09	2021-09-14 21:55:44	2021-04-28 12:35:21	23989

Data cleaning

After skimming the dataset, we took the below steps to clean the raw data :

Removing NA values
Removing outliers (out of \([25\%-1.5\times IQR,75\%+1.5\times IQR]\))
Transforming certain datatype into factor
Removing problematic entries (some people under 18 years old have more than 18 years experience)
Selecting key industries from 1000+ industries reported
Unifying currencies

Removing NA values

# remove the NA values and 0 salaries
ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  filter(!gender %in% c("NA","Other or prefer not to answer","Prefer not to answer", "Non-binary", NA) &
           race!="NA" &
           highest_level_of_education_completed!="NA"&
           annual_salary>0)

Removing outliers

# using z-score. remove data out of 3 sigma
# ask_a_manager_2021 <- ask_a_manager_2021[-which(abs(scale(ask_a_manager_2021$annual_salary))>3),]

# using quantile. remove data larger than 75%+1.5*IQR or smaller than 25%-1.5*IQR
# we choose this method recommended by the stats community
Q <- quantile(ask_a_manager_2021$annual_salary, probs=c(.25, .75))
iqr <- IQR(ask_a_manager_2021$annual_salary)
up <-  Q[2]+1.5*iqr # Upper Range
low <-  Q[1]-1.5*iqr # Upper Range
ask_a_manager_2021 <- ask_a_manager_2021 %>%
  filter(annual_salary>=low & annual_salary<=up)

Removing very small age group

We observe there are only 2 samples under 18 years old correctly entered their data, so we remove them to make analysis between age groups possible.

ask_a_manager_2021 %>% 
  group_by(how_old_are_you, gender) %>% 
  summarise(count=n()) %>% 
  ggplot(aes(x=fct_relevel(how_old_are_you,levels=c("under 18","18-24","25-34","35-44","45-54","55-64","65 or over")),y=count))+
  geom_col()+
  labs(title="Sample size in age groups",
       x="Age Group",
       y="number of samples")+
  NULL

ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  filter(how_old_are_you!="under 18")

Transforming into ordered `factor` datatype

Namely, we want to make age, years of working experience, education into factor, and take the log of salary for the next step of EDA.

ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  mutate(
    country = countrycode::countryname(country),
    age_group = factor(how_old_are_you,levels=c("18-24","25-34","35-44","45-54","55-64","65 or over")),
    field_exp = factor(years_of_experience_in_field,levels=c("1 year or less","2 - 4 years","5-7 years","8 - 10 years","11 - 20 years","21 - 30 years","31 - 40 years","41 years or more")),
    pro_exp = factor(overall_years_of_professional_experience,levels=c("1 year or less","2 - 4 years","5-7 years","8 - 10 years","11 - 20 years","21 - 30 years","31 - 40 years","41 years or more")),
    education = factor(highest_level_of_education_completed, levels=c("High School","Some college","College degree","Master's degree","Professional degree (MD, JD, etc.)", "PhD")),
     higher_edu = ifelse(education %in% c("College degree","Master's degree", "PhD", "Professional degree (MD, JD, etc.)"),1,0),
    salary = annual_salary,
    # take ln() to annual salary
    log_salary = log(annual_salary)
  ) %>% 
  janitor::clean_names() # clean columns names

Remove problematic entries

# there are people under 18 having more than 18 years of experience
ask_a_manager_2021 %>% 
  filter(age_group=="under 18") %>% 
  select(c("age_group","overall_years_of_professional_experience"))

age_group	overall_years_of_professional_experience

ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  mutate(max_age = case_when(how_old_are_you=="under 18"~18,
                             how_old_are_you=="65 or over"~999,
                             T~as.numeric(substr(how_old_are_you,4,5))),
         # parse the first number in a character
         min_exp = if_else(parse_number(overall_years_of_professional_experience)>
                       parse_number(years_of_experience_in_field),
                       parse_number(overall_years_of_professional_experience),
                       parse_number(years_of_experience_in_field))) %>% 
  # delete the problematic entries and the tow columns created here.
  filter(max_age>=min_exp) %>% 
  select(-c("max_age","min_exp"))

Selecting industries

Since there are over 1000 reported industries in the dataset, we will only keep the top 25 industries which account for 92% of total entries

# Industry is messy... it has > 1000 different industries.
# we only keep the names of top 25 industries. (24597(92%) out of 26765 entries)
industry_list <- ask_a_manager_2021 %>% 
  count(industry, sort=TRUE) %>% 
  mutate(percent = 100* n/sum(n)) %>% 
  slice_max(order_by = n, n = 25) %>% 
  select(industry)

ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  mutate(industry = ifelse(industry %in% industry_list$industry,
                           industry,
                           "Others"))

Unifying currencies

Since there are 11 different currencies reported in the dataset, we want to unify the most common currencies into USD for the convenience of comparison analysis afterwards. We decided to convert all currencies with occurences greater than 100 into USD. This included CAD,GBP,EUR,AUD/NZD. Other was not converted as there wasn’t specific information on the currency.

ask_a_manager_2021 %>%
  count(currency, sort=TRUE) %>%
  mutate(percent = 100* n/sum(n))

currency	n	percent
USD	20268	83.6
CAD	1474	6.08
GBP	1434	5.91
EUR	551	2.27
AUD/NZD	432	1.78
Other	57	0.235
CHF	29	0.12
SEK	1	0.00412

From the above table, We can see that USD, CAD, GBP, EUR, (AUD/NZD) are the most common currencies. We will convert the currencies all to USD using exchange rate data from library quantmod, and the exchange rate will be taken from the last date of the survey “2021-09-14”

#gets the currency rate for the currency pairs. This uses the Oanda which keeps currency data for the last 180 days.
#In 180 days from "2021-09-14" the code will no longer return the currency rates.
currencies <-getSymbols(c("EUR/USD","CAD/USD","GBP/USD","AUD/USD" , "NZD/USD"),
                        from="2021-09-14", to="2021-09-14", src="oanda")

#In order to preserve the analysis for after 180 days we can hard code the currency rates into a tibble
currencies_preserved <- tibble(
  name = c("EUR/USD","CAD/USD","GBP/USD","AUD/USD" , "NZD/USD"),
  value = c(1.18,0.79,1.38,0.734,0.711)
)

Here we create a new column called converted_salary which converts the 5 most common currencies in USD. These are then rounded to the nearest whole number.

#the values are taken from the currencies_preserved$value as to preserve the analysis when 
# getSymbols will no longer work. The index matches the currency pair.
ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  mutate(converted_salary = case_when(
    currency == "GBP" ~ round(annual_salary*currencies_preserved$value[3]),
    currency == "AUD/NZD" & country == "Australia" ~ round(annual_salary*currencies_preserved$value[4]),
    currency == "AUD/NZD" & country == "New Zealand" ~ round(annual_salary*currencies_preserved$value[5]),
    currency == "CAD" ~ round(annual_salary*currencies_preserved$value[2]),
    currency == "EUR" ~ round(annual_salary*currencies_preserved$value[1]),
    TRUE ~ round(annual_salary)
  ))

#Here we filter the dataset to only include the salaries that were converted into USD terms. The other currencies also included lots of outliers which we also get rid of here.

ask_a_manager_2021 <- ask_a_manager_2021 %>% 
  filter(currency %in% c("USD","GBP","AUD/NZD","EUR","CAD") &
           !is.na(country))

ask_a_manager_2021 %>%
  count(currency, sort=TRUE) %>%
  mutate(percent = 100* n/sum(n))

currency	n	percent
USD	20128	84.1
CAD	1464	6.12
GBP	1362	5.69
EUR	547	2.29
AUD/NZD	428	1.79

Exploratory Data Analysis

Counts

# Some quick counts, groups, etc
ask_a_manager_2021 %>% 
  count(age_group, sort=TRUE) %>% 
  mutate(percent = 100* n/sum(n)) %>% 
  ggplot(aes(x=fct_relevel(age_group,levels=c("under 18","18-24","25-34","35-44","45-54","55-64","65 or over")), y=n)) +
  geom_bar(stat="identity") + 
  labs(title = "Age distribution of Ask a Manager survey respondents",
       x="Age group",
       y="Frequency",                                                  
       caption = "Source:Askamanager.com")

# 'country' 
ask_a_manager_2021 %>%
  count(country, sort=TRUE) %>% 
  mutate(percent = 100* n/sum(n))

# 'city' 
ask_a_manager_2021 %>% 
  count(city, sort=TRUE) %>% 
  mutate(percent = 100* n/sum(n))

# education 
ask_a_manager_2021 %>% 
  count(education) %>% 
  mutate(percent = 100* n/sum(n))%>% 
  arrange(desc(percent))

# gender
ask_a_manager_2021 %>% 
  count(gender) %>% 
  mutate(percent = 100* n/sum(n))%>% 
  arrange(desc(percent))

# race
ask_a_manager_2021 %>% 
  count(race) %>% 
  mutate(percent = 100* n/sum(n))%>% 
  arrange(desc(percent))

# pro_exp 
ask_a_manager_2021 %>% 
  count(pro_exp ) %>% 
  mutate(percent = 100* n/sum(n))%>% 
  arrange(desc(percent))

# field_exp  
ask_a_manager_2021 %>% 
  count(field_exp) %>% 
  mutate(percent = 100* n/sum(n))%>% 
  arrange(desc(percent))

#make comments about the counts

Salary

How is salary distributed?

favstats(ask_a_manager_2021$salary) # find a really rich guy here

min	Q1	median	Q3	max	mean	sd	n	missing
1	5.4e+04	7.5e+04	1.04e+05	1.92e+05	8.18e+04	3.75e+04	23929	0

# density
g1 <- ggplot(ask_a_manager_2021, aes(x=salary))+
  geom_density()+
  NULL
#cdf
g2 <- ask_a_manager_2021 %>% 
  slice_min(order_by = salary,n =nrow(ask_a_manager_2021)-5) %>% # choose a number
  ggplot(aes(x=salary))+
  stat_ecdf()+
  NULL

# taking log is better
g3 <- ggplot(ask_a_manager_2021, aes(x=log(salary)))+
  geom_density()+
  NULL

g4 <- ask_a_manager_2021 %>% 
  slice_min(order_by = salary,n =nrow(ask_a_manager_2021)-5) %>% # choose a number
  ggplot(aes(x=log(salary)))+
  stat_ecdf()+
  NULL

gridExtra::grid.arrange(g1,g2,g3,g4)

Observation: This is a right skewed distribution.

Industry

ask_a_manager_2021 %>% 
  count(industry, sort=TRUE) %>% 
  ggplot(aes(y=fct_reorder(industry,n), x=n))+
  geom_col()

Observations:

Computing & tech is the top-chosen industry among respondents, followed by Education and Non-profit
This indicate that the sample might include more respondents from industries have higher exposure to tech and internet.

Salary ,Gender and Industry

We are interested in the type of industries with top salary for man and woman.

# Industries of top average salary for Man and Woman
salary_table <- ask_a_manager_2021 %>% 
  group_by(industry, gender) %>% 
  summarise(count = n(),
            avg_salary = mean(converted_salary),
            higher_edu_prop = sum(higher_edu)/n()) %>% 
  pivot_wider(id_cols = 1:5,
              names_from = gender,
              values_from = count:higher_edu_prop)
  
g_man <- salary_table %>% 
  ggplot(aes(y=fct_reorder(industry,avg_salary_Man), x=avg_salary_Man,fill=higher_edu_prop_Man))+
  geom_bar(position="dodge", stat="identity")+
  geom_text(aes(label=paste(avg_salary_Man%/%1000,"k")),
            position=position_dodge(width=0.9), hjust=0,vjust=0)+
  scale_x_continuous(labels = scales::comma) +
  scale_fill_gradient(low="sky blue", high="blue")+
  labs(
    title="Man",
    x="Annual Salary $",
    y="Industry",
    fill="Higher Education %"
  )+
  theme_wsj()+
  theme(legend.position="bottom",
        legend.title=element_text(size=13))+
  NULL

ggsave("highest_paid_industries_male.png",width = 12,height = 8,limitsize = F)
g_woman <- salary_table %>% 
  ggplot(aes(y=fct_reorder(industry,avg_salary_Woman), x=avg_salary_Woman,fill=higher_edu_prop_Woman))+
  geom_bar( position="dodge", stat="identity")+
  geom_text(aes(label=paste(avg_salary_Woman%/%1000,"k")),
              position=position_dodge(width=0.9), hjust=0,vjust=0)+
  scale_x_continuous(labels = scales::comma) +
  scale_fill_gradient(low="pink", high="red")+
  labs(
    title="Woman",
    x="Annual Salary $",
    y="Industry",
    fill="Higher Education %"
  )+
  theme_wsj()+
  theme(legend.position="bottom",
        legend.title=element_text(size=13))+
  NULL


ggsave("highest_paid_industries_female.png",width = 12,height = 8,limitsize = F)

g_man

g_woman

Observations:

For both man and woman, the top earning industries are alike (Law, Computing or Tech, Business or Consulting)
Respondents from Law, Govenment and Education tends to have higher education level compared to the rest, reflecting the academic/professional requirements of these positions
The difference between the salary within sales and accounting, banking & finance is likely due to the subdivisions chosen based on gender nature

We are also interested in the salary difference between man and woman within the same industry.

# salary gap in different industries
ask_a_manager_2021 %>% 
  group_by(industry, gender) %>% 
  summarise(count = n(),
            avg_salary = mean(converted_salary)) %>% 
  pivot_wider(id_cols = 1:4,
              names_from = gender,
              values_from = count:avg_salary) %>% 
  mutate(size = count_Man+count_Woman,
         male_prop = count_Man/(count_Man+count_Woman),
         salary_gap = avg_salary_Man - avg_salary_Woman) %>% 
  ggplot(aes(y=fct_reorder(industry,salary_gap), x=salary_gap,fill=male_prop))+
  geom_col()+
  
  # geom_point(aes(y=fct_reorder(industry,size),x=size*10))+
  
  scale_x_continuous(
    breaks = seq(-20000,40000,5000)
  ) +
  scale_fill_gradient(low="pink", high="blue")+
  labs(
    title="Salary Gap and Sex Ratio",
    x="Salary Gap in $",
    y="",
    fill="Male %"
  )+
  theme_bw()+
  theme(legend.position="bottom",
        legend.title=element_text(size=8))+
  NULL

ggsave("salary_gap.png",width = 12,height = 8,limitsize = F)

Observations:

Man has a higher average salary than woman in most of the industries, with Law being the most significant
Woman has higher average salary in Art & Design
The proportion of male within computing or tech is significantly higher than that within other industries; yet the proportion only reaches c. 40%, reflecting the fact that most respondents are female because Ask_a_manager is more popular among women
The proportion of male is also higher in labour-intensive industries such as transport or logistics, engineering, utilities & telecommunications

Education

Next, we want to see if there is a difference in the salary gap between man and woman for different education level.

ask_a_manager_2021 %>% 
  group_by(education, gender) %>% 
  summarise(count = n(),
            avg_salary = mean(converted_salary)) %>% 
  pivot_wider(id_cols = 1:4,
              names_from = gender,
              values_from = count:avg_salary) %>% 
  mutate(size = count_Man+count_Woman,
         male_prop = count_Man/(count_Man+count_Woman),
         salary_gap = avg_salary_Man - avg_salary_Woman) %>% 
  ggplot(aes(x=education, y=salary_gap,fill=male_prop))+
  geom_col()+
  scale_y_continuous(
    breaks = seq(-20000,40000,5000)
  ) +
  scale_fill_gradient(low="pink", high="sky blue")+
  theme_bw()+
  theme(legend.position="bottom", axis.title=element_text(size=8))+
  ggtitle("Salary Gap at Different Education level") +
  xlab("Education Level") + ylab ("Salary Gap in $") + 
  scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
  NULL

ggsave("salary_gap_by_edu.png",width = 14,height = 8,limitsize = F)

ask_a_manager_2021 %>% 
  filter(gender %in% c("Man", "Woman")) %>% 
  mutate(sex = factor (gender, labels = c("Man", "Woman"))) %>% 
  rename(Education = education) %>% 
  group_by(Education, gender) %>% 
  summarise (median_salary_by_edu = median (converted_salary),
             mean_salary_by_edu = mean(converted_salary), ) %>% 
  ggplot () +
  geom_col(aes (Education, median_salary_by_edu, fill = gender), position = position_dodge(width = 0.9), alpha = 0.7)+
#Removed the section which broke the code
  scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
  NULL

Race

Count

ask_a_manager_2021 %>% 
  group_by(race) %>% 
  filter(n() > 500) %>% 
  summarise(count=n()) %>% 
  ggplot(aes(y=count, x=race, fill=race))+
  geom_col() +
  theme_wsj()+
  theme(legend.position = "none") +
  xlab("Race") + ylab ("Count") + 
  labs(title="Count by Race", subtitle = "Races with > 500 Respondents")+
  scale_x_discrete(labels = function(x) str_wrap(x, width = 10)) + 
  NULL

Race and Mean Salary

ask_a_manager_2021 %>% 
  filter(industry %in% industry_list$industry) %>% 
  group_by(race) %>% 
  filter(n() > 500) %>% 
 ggplot( aes(x=race, y=converted_salary, color=race)) +
    geom_jitter(color="black", size=0.01, alpha=0.9) +
   geom_boxplot(alpha=0.4) +
   scale_fill_viridis(discrete = TRUE, alpha=0.6) +
    geom_hline(yintercept=144988, color="red") +
    theme(
      legend.position="none",
      plot.title = element_text(size=11)
    ) +
    theme_wsj() +
    theme(legend.position = "none")+
    theme(axis.title=element_text(size=10))+
    ggtitle("Salary Vs. Race Boxplot") +
    ylab("Salary") + xlab ("Race") +
    scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
    scale_y_continuous(labels = scales::comma, limits = c(0, 300000)) +
    NULL

Observation: In our boxplot one can visualize both the distribution of the data and the medium and interquartile ranges of the data. When comparing annual salary by race, our data shows that Asians have the higher salaries in comparison to Black and African American and White sample respondents. Interestingly enough, our sample also shows that the medium salary for Black and AA respondents is higher than that of White respondents.

Since most repondents were white, the larger sample size is less prone to skewness due to outliers when comparing it to the other two races portrayed in the plot.

ask_a_manager_2021_race <- ask_a_manager_2021 %>%
  group_by(race) %>% 
  filter(race %in% c("Black or African American", "White")) 

t.test(salary ~ race, data = ask_a_manager_2021_race)

## 
##  Welch Two Sample t-test
## 
## data:  salary by race
## t = 0.6, df = 610, p-value = 0.5
## alternative hypothesis: true difference in means between group Black or African American and group White is not equal to 0
## 95 percent confidence interval:
##  -2140  4021
## sample estimates:
## mean in group Black or African American                     mean in group White 
##                                   81976                                   81035

Observation:

When running a T-test on the two racial groups, White and Black or African American, the P-value we get is 0.9. Thus there is no statistically signifcant difference in their annual salary when calculating it based of off this data set.

Location

#create df of the list of states with >10 occurrences 
#This allows us to get data for actual states as many data entry errors
#many individuals put multiple states and this helps to fix that
states <- ask_a_manager_2021 %>% 
  group_by(state) %>%
  filter(!is.na(state)) %>%
  filter(n()>10) %>% 
  summarise(mean_salary = mean(salary),
            count_state = count(state))

states$fips <- fips(states$state)
statesalarymap <- states %>% select(state,mean_salary)

plot_usmap(data=statesalarymap, values="mean_salary", color="black") + scale_fill_continuous(
    low = "white",
    high = "light green",
    name = "Mean Salary") +
  theme(legend.position = "right") +
  labs(title="Map of US States based on Average Salary")

# Count by Industry

ask_a_manager_2021 %>% 
  group_by(industry) %>% 
  summarise(count=n()) %>% 
  ggplot(aes(y=fct_reorder(industry,count),x=count))+
  geom_col()

# Count by Age Group
ask_a_manager_2021 %>% 
  group_by(age_group) %>% 
  summarise(count=n()) %>% 
  ggplot(aes(y=fct_reorder(age_group,count),x=count))+
  geom_col()

# Sorting out the people who are 18+ 
ask_a_manager_age <- ask_a_manager_2021 %>%  
                    mutate(factor(age_group,levels=c("18-24","25-34","35-44","45-54","55-64","65 or over")))

#there are only 6 women in under 18 category so excluding them for the graph since there is no male data in that category to compare
ask_a_manager_age %>% 
  filter(age_group %in% c("18-24", "25-34" , "35-44" , "45-54" , "55-64"  )) %>% 
  group_by(age_group, gender) %>% 
  summarise (median_salary_by_age = median (salary),
             mean_salary_by_age = mean(salary)) %>% 
  ggplot () +
  geom_col(aes (age_group, median_salary_by_age, fill = gender), position = position_dodge(width = 0.9), alpha = 0.7)+
  geom_point(aes(x = age_group, y=mean_salary_by_age, color = gender))+
  theme_bw()+
  #formatC(x, format = "d")+
  labs(title =  "Median Salary by Age Group" , y="Salary" ,x = "Age Group", subtitle = "Points represent mean salary") +
  scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
  NULL

Changed Industry? vs salary

ask_a_manager_2021_changed <- ask_a_manager_2021  %>%
mutate(if_changed= if_else(overall_years_of_professional_experience == years_of_experience_in_field, "No", "Yes"))

ask_a_manager_2021_changed %>% 
ggplot(aes(x=fct_relevel(overall_years_of_professional_experience,levels=c("1 year or less","2 - 4 years","5-7 years","8 - 10 years","11 - 20 years","21 - 30 years","31 - 40 years","41 years or more")), y=annual_salary, color=if_changed))+
  # scatter plot
  geom_point(alpha = 0.5)+
  # linear smooth line
  geom_smooth(method = "lm")+
  # legend settings
  theme(legend.position = "bottom",
        legend.title = element_blank())+
  labs(title="Whether changing job affects your salary",
       x="Total Years Spent Working",
       y="Salary")+
  theme_bw()+
  scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
  NULL

ask_a_manager_2021_changed %>% 
  group_by(overall_years_of_professional_experience, if_changed) %>% 
  summarise (median_salary_over_time = median (salary),
             mean_salary_over_time = mean(salary)) %>% 
  ggplot () +
  geom_col(aes (fct_relevel(overall_years_of_professional_experience,levels=c("1 year or less","2 - 4 years","5-7 years","8 - 10 years","11 - 20 years","21 - 30 years","31 - 40 years","41 years or more")), median_salary_over_time, fill=if_changed), position = position_dodge(width = 0.9), alpha = 0.7)+
  geom_point(aes(x = overall_years_of_professional_experience, y=mean_salary_over_time, color = if_changed))+
  theme_bw()+
   scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
  #formatC(x, format = "d")+
  labs(  title =  "Median Salary over time" , y="Salary" ,x = "Prof", subtitle = "Points represent the mean") +
  NULL

ggsave("switch_industry.png",width = 12,height = 8,limitsize = F)

Observation:

The greater the amount of experience the greater salary difference between those who switch and those who don’t.
The percentage increase in salary with increasing professional experience is proportional.
The outliers for the data were predominantly those who switched industry.

Statistical Tests

Gender vs Salary

General Statistics & Boxplot

mosaic::favstats (converted_salary ~ gender, data=ask_a_manager_2021)

gender	min	Q1	median	Q3	max	mean	sd	n	missing
Man	1	6.3e+04	9e+04	1.28e+05	2.62e+05	9.67e+04	4.3e+04	4303	0
Woman	35	5.25e+04	7.11e+04	9.7e+04	2.55e+05	7.82e+04	3.48e+04	19626	0

ask_a_manager_2021 %>% 
  ggplot( aes(x=gender, y=converted_salary, color=gender)) +
    geom_jitter(color="black", size=0.4, alpha=0.9) +
    geom_boxplot(alpha=0.3) +
    scale_fill_viridis(discrete = TRUE, alpha=0.6) +
    theme_wsj() +
    theme(
      legend.position="none",
      plot.title = element_text(size=11)
    ) +
   theme(
      legend.position="none",
      plot.title = element_text(size=11)
    ) +
    theme(axis.title=element_text(size=12))+
    ggtitle("Salary Vs. Gender Boxplot with Jitter") +
    ylab("Salary") + xlab ("Race") + 
    scale_x_discrete(labels = function(x) str_wrap(x, width = 10))+
    scale_y_continuous(labels = scales::comma, limits = c(0, 300000)) +
    NULL

For our following analysis, we will be comparing data from the male gender “Man” with data from the female gender “Woman.” We will filter out the data on those that are non binary.

T-Test

ask_a_manager_2021 <- ask_a_manager_2021 %>%
  filter(gender!="Non-binary")
t.test(converted_salary ~ gender, data = ask_a_manager_2021)

## 
##  Welch Two Sample t-test
## 
## data:  converted_salary by gender
## t = 26, df = 5602, p-value <2e-16
## alternative hypothesis: true difference in means between group Man and group Woman is not equal to 0
## 95 percent confidence interval:
##  17124 19871
## sample estimates:
##   mean in group Man mean in group Woman 
##               96721               78223

Observation: This T.test proves there is a statistically significant difference in salary between man and woman.

Confidence Intervals

#mosaic::favstats (annual_salary ~ gender, data=ask_a_manager_2021)
ask_a_manager_2021_gender <- ask_a_manager_2021 %>%
  mutate(gender2 = case_when(
  gender  == "Man" ~ "1",
 gender == "Woman" ~ "0",
  TRUE ~ "NA"
)) %>%
  mutate(gender2 = as.numeric(gender2))


mosaic::favstats (converted_salary ~ gender, data=ask_a_manager_2021_gender) %>%
mutate(t_critical = qt(0.975,n-1),
         sd_mean = sd/sqrt(n),
         margin_of_error = t_critical*sd_mean,
         ci_lower = mean-margin_of_error,
         ci_higher = mean+margin_of_error)

gender	min	Q1	median	Q3	max	mean	sd	n	missing	t_critical	sd_mean	margin_of_error	ci_lower	ci_higher
Man	1	6.3e+04	9e+04	1.28e+05	2.62e+05	9.67e+04	4.3e+04	4303	0	1.96	655	1.28e+03	9.54e+04	9.8e+04
Woman	35	5.25e+04	7.11e+04	9.7e+04	2.55e+05	7.82e+04	3.48e+04	19626	0	1.96	248	487	7.77e+04	7.87e+04

Observation: Since two 95% confidence intervals do not overlap, we are at least 95% confident that the male have higher salary than the female on average.

Bootstrap Test

# hypothesis testing using infer package
diff <- ask_a_manager_2021_gender %>%
  specify(converted_salary ~ gender) %>%
  calculate(stat = "diff in means", order = c("Woman", "Man"))

set.seed(1234)
salary_in_null_world <- ask_a_manager_2021_gender %>%
  filter(gender !="Non-binary") %>%
  specify(converted_salary ~ gender) %>%
   # assuming independence of gender and salary
  hypothesize(null = "independence") %>%
   # generate 1000 reps, of type "permute"
  generate(reps = 1000, type = "permute") %>%
  # calculate statistic of difference, namely "diff in means"
   calculate(stat = "diff in means", order = c("Woman", "Man")) 

salary_in_null_world %>% 
  visualise()+
  shade_p_value(obs_stat = diff, direction = "two-sided")

p_value <- salary_in_null_world %>% 
  get_pvalue(obs_stat = diff, direction="both")
p_value

p_value
0

Observation: Our null hypothesis is that the difference of annual salaries between male and female is 0 and we get a p_value very close to 0. Therefore we reject the null hypothesis with 95% confidence. There is difference between the average male and female salary.

Gender vs Education

We want to look at the relationship between one’s gender and education degree. In essence, we want to explore if there is a difference in the proportion of respondents with high school degree as their highest degree for male group and the female group. We can use the proportion test to generate the result from the male and female sample.

ask_a_manager_2021_education <- ask_a_manager_2021 %>% 
   filter(gender !="Non-binary") %>%
   mutate(below_college = if_else(highest_level_of_education_completed %in% c("High School", "Some college"), "Yes", "No")) %>% 
   group_by(gender) %>% 
   summarise(college_below=sum(below_college == "Yes"), college_or_above = sum(below_college == "No"))

ask_a_manager_2021_education

gender	college_below	college_or_above
Man	635	3668
Woman	1579	18047

prop.test(x = c(3668,18047), n = c(3668+635,18047+1579), alternative = "two.sided")

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c out of c3668 out of 3668 + 63518047 out of 18047 + 1579
## X-squared = 189, df = 1, p-value <2e-16
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.0785 -0.0557
## sample estimates:
## prop 1 prop 2 
##  0.852  0.920

From the result of proportion test for male group and female group, we are 99% confident that the proportion of high school as highest education level for male is higher than that for female, indicating that overall female has a higher college-entry rate vs. the male.

If we repeat the process to explore the difference in proportion in acquiring a masters or above degree for both gender:

ask_a_manager_2021_education <- ask_a_manager_2021 %>% 
  filter(gender !="Non-binary") %>%
  mutate(higher_edu = if_else(highest_level_of_education_completed %in% c("Master's degree", "Professional degree (MD, JD, etc.)", "PhD"), "Yes", "No")) %>% 
  group_by(gender) %>% 
  summarise(master_below = sum(higher_edu == "No"), master_or_above=sum(higher_edu == "Yes") )


ask_a_manager_2021_education

gender	master_below	master_or_above
Man	2811	1492
Woman	11068	8558

prop.test(x = c(1492, 8558), n = c(1492+2811, 8558+11068), alternative = "two.sided")

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c out of c1492 out of 1492 + 28118558 out of 8558 + 11068
## X-squared = 115, df = 1, p-value <2e-16
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.1053 -0.0734
## sample estimates:
## prop 1 prop 2 
##  0.347  0.436

From the result of two proportion tests, we can see that even though the proportion of acquiring a college-or-above degree is less in the male group, the proportion of acquiring higher education degree (Master’s-or-above) is higher than the female group. This somehow explains the fact that there are more outliers in male sample with extremely high income level.

Race vs Salary

Here we want to see if race is affecting the salary.

ask_a_manager_salary <- ask_a_manager_2021 %>% 
  mutate(if_white = if_else(race == "White", "Yes", "No")) %>% 
  select(if_white,salary)
t.test(salary~if_white, data = ask_a_manager_salary, success = "Yes")

## 
##  Welch Two Sample t-test
## 
## data:  salary by if_white
## t = 7, df = 4948, p-value = 4e-12
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  3474 6195
## sample estimates:
##  mean in group No mean in group Yes 
##             85869             81035

Race vs Education

We want to look at the relationship between one’s race and education degree. Particularly, we want to see if there is a difference in education level for those being white and those being non-white.

As the above analysis for gender vs. education, we run two proportion tests for college-or-above degree percentage and master-or-above percentage between the male and female group.

ask_a_manager_2021_race <- ask_a_manager_2021 %>% 
  mutate(if_white = if_else(race == "White", "White", "Non-white"),
         below_college = if_else(highest_level_of_education_completed %in% c( "High School", "Some college"), "Yes", "No")) %>% 
  group_by(if_white) %>% 
  summarise(college_below=sum(below_college == "Yes"), college_or_above = sum(below_college == "No"))

ask_a_manager_2021_race

if_white	college_below	college_or_above
Non-white	334	3333
White	1880	18382

prop.test(x = c(3333,18382), n = c(3333+334, 18382+1880), alternative = "two.sided")

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c out of c3333 out of 3333 + 33418382 out of 18382 + 1880
## X-squared = 0.09, df = 1, p-value = 0.8
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.00859  0.01200
## sample estimates:
## prop 1 prop 2 
##  0.909  0.907

Similarly, if we run the test for the propotion of master_or_above education level between white and non-white races:

ask_a_manager_2021_race <- ask_a_manager_2021 %>% 
  mutate(if_white = if_else(race == "White", "White", "Non-white"),
         higher_edu = if_else(highest_level_of_education_completed %in% c("Master's degree", "Professional degree (MD, JD, etc.)", "PhD"), "Yes", "No")) %>% 
  group_by(if_white) %>% 
  summarise(master_below = sum(higher_edu == "No"), master_or_above=sum(higher_edu == "Yes") )

ask_a_manager_2021_race

if_white	master_below	master_or_above
Non-white	2256	1411
White	11623	8639

prop.test(x = c(1411, 8639), n = c(1411+2256, 8629+11623), alternative = "two.sided")

## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c out of c1411 out of 1411 + 22568639 out of 8629 + 11623
## X-squared = 22, df = 1, p-value = 3e-06
## alternative hypothesis: two.sided
## 95 percent confidence interval:
##  -0.0591 -0.0245
## sample estimates:
## prop 1 prop 2 
##  0.385  0.427

Observation: From the result of the proportion test, we cannot see a clear difference between the proportion of education level in white and non-white group, as the p-value is higher than 5%.

However, the proportion of acquiring higher education degree (Master’s-or-above) is higher in the white group vs. other races

Changed Industry? vs salary T.Test

t.test(salary~if_changed, data = ask_a_manager_2021_changed)

## 
##  Welch Two Sample t-test
## 
## data:  salary by if_changed
## t = 19, df = 23826, p-value <2e-16
## alternative hypothesis: true difference in means between group No and group Yes is not equal to 0
## 95 percent confidence interval:
##  7949 9827
## sample estimates:
##  mean in group No mean in group Yes 
##             85884             76996

ask_a_manager_age %>% 
  filter(age_group %in% c("18-24", "25-34" , "35-44" , "45-54" , "55-64"  )) %>% 
  group_by(age_group, gender) %>% 
  summarise (median_salary_by_age = median (salary),
             mean_salary_by_age = mean(salary)) %>% 
  ggplot () +
  geom_col(aes (age_group, median_salary_by_age, fill = gender), position = position_dodge(width = 0.9), alpha = 0.7)+
  geom_point(aes(x = age_group, y=mean_salary_by_age, color = gender))+
  theme_bw()+
  #formatC(x, format = "d")+
  labs(  title =  "Median Salary by Age Group" , y="Salary" ,x = "Age Group") +
  NULL

Observation:

Changing industry has a statistically significant affect in average salary in our respondent sample. Those who change salary earn less, in general.

Regression Analysis

# load population data of US
population_url <- "https://www.ers.usda.gov/webdocs/DataFiles/48747/PopulationEstimates.csv?v=2232"
population <- vroom(population_url) %>% 
  janitor::clean_names() %>% 
  
  # select the latest data, namely 2019
  select(fips = fip_stxt, state= area_name, pop_estimate_2019) %>% 
  group_by(state) %>% 
  summarise(pop_estimate_2019_m = sum(pop_estimate_2019)/1000000)

reg_data <- ask_a_manager_2021 %>% 
  filter(!is.na(state)&industry %in% industry_list$industry[1:15]) %>%
  group_by(state) %>%
  filter(n()>10) %>% 
  ungroup() %>% 
  filter(country =="US"&currency=="USD") %>% 
  mutate(job = tolower(job_title),
         research=grepl("research", job),
         manager=grepl("manager", job),
         engineer=grepl("engineer", job),
         analyst=grepl("analyst", job),
         data_related = grepl("data", job),
         scientist = grepl("scientist", job),
         database = grepl("database", job),
         librarian = grepl("librarian", job),
         add_context_job = !is.na(additional_context_on_job_title),
         add_context_inc = !is.na(additional_context_on_income),
         race = case_when(race=="White"~"White",
                           race=="Asian or Asian American"~"Asian",
                           race=="Black or African American"~"Black",
                           T~"Others"),
         ) %>% 
  left_join(population,by = c("state")) %>% 
  select(c("age_group","gender","education","field_exp","pro_exp","race",
           "salary","research","manager","engineer","industry","analyst",
           "data_related","scientist","database","librarian","add_context_job",
           "add_context_inc","pop_estimate_2019_m"))
set.seed(1234)
data_split <- initial_split(reg_data, prop = .7)
data_train <- training(data_split)
data_test  <- testing(data_split)

m1 <- lm(salary ~ age_group, data=data_train)
m2 <- lm(salary ~ pro_exp, data=data_train)
m3 <- lm(salary ~ field_exp, data=data_train)

huxreg(m1, m2, m3,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma',
                      "AIC" = "AIC"), 
       bold_signif = 0.05, 
       stars = NULL
) %>% 
  set_caption('Comparison of models (age or experience?)')

Comparison of models (age or experience?)
	(1)	(2)	(3)
(Intercept)	61635.571	69671.994	65433.717
	(1832.014)	(2855.294)	(1625.252)
age_group25-34	20407.709
	(1904.286)
age_group35-44	30716.137
	(1921.989)
age_group45-54	33106.375
	(2096.570)
age_group55-64	22772.191
	(2587.712)
age_group65 or over	30382.329
	(5556.773)
pro_exp2 - 4 years		1345.220
		(3057.459)
pro_exp5-7 years		8494.468
		(2973.095)
pro_exp8 - 10 years		16057.951
		(2961.636)
pro_exp11 - 20 years		22547.278
		(2914.158)
pro_exp21 - 30 years		27128.221
		(3013.121)
pro_exp31 - 40 years		21967.309
		(3475.103)
pro_exp41 years or more		18277.526
		(5948.339)
field_exp2 - 4 years			6838.122
			(1781.163)
field_exp5-7 years			17214.794
			(1763.885)
field_exp8 - 10 years			25866.721
			(1810.061)
field_exp11 - 20 years			32427.263
			(1767.441)
field_exp21 - 30 years			40462.832
			(2095.928)
field_exp31 - 40 years			32929.075
			(3288.613)
field_exp41 years or more			41222.125
			(8428.581)
#observations	11366	11366	11366
R squared	0.036	0.047	0.090
Adj. R Squared	0.036	0.046	0.089
Residual SE	37095.450	36898.532	36049.843
AIC	271432.355	271313.361	270784.405

# add more variables to explore and improve accuracy
m4 <- lm(salary ~ field_exp+gender, data=data_train)
m5 <- lm(salary ~ field_exp+gender+gender*field_exp, data=data_train)
m6 <- lm(salary ~ field_exp+gender+education, data=data_train)
m7 <- lm(salary ~ field_exp+gender+gender*field_exp+education+race, data=data_train)
m8 <- lm(salary ~ field_exp+gender+gender*field_exp+education+race+pop_estimate_2019_m, data=data_train)
m9 <- lm(salary ~ field_exp+gender+gender*field_exp+education+race+pop_estimate_2019_m++research+manager+engineer+industry+data_related+scientist+database+librarian, data=data_train)
m10 <- lm(salary ~ field_exp+gender+gender*field_exp+education+race+pop_estimate_2019_m++research+manager+engineer+industry+data_related+scientist+database+librarian+add_context_job+add_context_inc, data=data_train)
m11 <- lm(salary ~ field_exp+gender+gender*field_exp+education+race+pop_estimate_2019_m++research+manager+engineer+industry+data_related+scientist+database+librarian+add_context_job+add_context_inc+data_related*scientist, data=data_train)

huxreg(m4, m5, m6, m7, m8, m9,m10,m11,
       statistics = c('#observations' = 'nobs', 
                      'R squared' = 'r.squared', 
                      'Adj. R Squared' = 'adj.r.squared', 
                      'Residual SE' = 'sigma',
                      "AIC" = "AIC"), 
       bold_signif = 0.05
) %>% 
  set_caption('Comparison of models (adding variables)')

Comparison of models (adding variables)
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
(Intercept)	82483.049 ***	69628.934 ***	61442.370 ***	68574.888 ***	57853.358 ***	42915.253 ***	43368.902 ***	43282.577 ***
	(1765.664)	(4507.873)	(3166.399)	(5296.351)	(5263.800)	(4598.579)	(4594.684)	(4594.386)
field_exp2 - 4 years	6196.971 ***	11580.886 *	5982.387 ***	13174.453 **	13505.674 **	10899.235 **	10947.596 **	11045.310 **
	(1743.832)	(4852.730)	(1703.013)	(4688.376)	(4627.460)	(3968.051)	(3963.290)	(3963.175)
field_exp5-7 years	16377.048 ***	27928.293 ***	16152.069 ***	29079.987 ***	29292.137 ***	26469.305 ***	26458.740 ***	26543.246 ***
	(1727.091)	(4796.247)	(1688.233)	(4633.690)	(4573.462)	(3922.239)	(3917.520)	(3917.328)
field_exp8 - 10 years	25199.227 ***	38864.445 ***	24544.398 ***	40456.388 ***	40503.349 ***	37719.869 ***	37833.908 ***	37957.127 ***
	(1772.137)	(4913.937)	(1733.477)	(4748.284)	(4686.551)	(4021.405)	(4016.630)	(4016.700)
field_exp11 - 20 years	31141.420 ***	47860.450 ***	31052.911 ***	49988.943 ***	50798.309 ***	46225.827 ***	46395.762 ***	46503.502 ***
	(1731.126)	(4768.854)	(1694.291)	(4608.543)	(4548.865)	(3905.641)	(3901.098)	(3901.069)
field_exp21 - 30 years	37525.013 ***	60021.389 ***	38730.943 ***	64272.212 ***	64767.293 ***	59023.009 ***	59130.650 ***	59252.556 ***
	(2055.960)	(5137.828)	(2011.519)	(4966.416)	(4901.929)	(4208.708)	(4203.698)	(4203.712)
field_exp31 - 40 years	30935.521 ***	46038.954 ***	32456.827 ***	49881.389 ***	51156.019 ***	43022.829 ***	43078.827 ***	43222.879 ***
	(3220.494)	(7399.567)	(3146.731)	(7153.386)	(7060.764)	(6079.513)	(6072.245)	(6072.030)
field_exp41 years or more	35440.467 ***	43913.566 ***	37627.381 ***	50078.983 ***	48625.778 ***	41841.212 ***	41905.812 ***	42027.137 ***
	(8254.891)	(13238.881)	(8059.436)	(12791.714)	(12625.683)	(10823.046)	(10810.091)	(10809.049)
genderWoman	-19462.346 ***	-4788.972	-21123.723 ***	-5613.328	-5308.446	3823.444	3746.403	3870.918
	(874.130)	(4816.323)	(858.022)	(4652.743)	(4592.285)	(3939.171)	(3934.651)	(3934.753)
field_exp2 - 4 years:genderWoman		-5812.696		-7175.929	-7008.995	-5215.950	-5146.048	-5235.200
		(5198.644)		(5022.080)	(4956.796)	(4249.195)	(4244.143)	(4243.921)
field_exp5-7 years:genderWoman		-13109.252 *		-13194.269 **	-13241.990 **	-10388.510 *	-10230.593 *	-10314.224 *
		(5139.849)		(4965.449)	(4900.892)	(4200.445)	(4195.502)	(4195.256)
field_exp8 - 10 years:genderWoman		-15637.001 **		-16538.217 **	-16070.142 **	-12689.203 **	-12650.008 **	-12762.324 **
		(5267.091)		(5088.890)	(5022.800)	(4306.057)	(4300.910)	(4300.829)
field_exp11 - 20 years:genderWoman		-19445.181 ***		-19952.011 ***	-20466.473 ***	-13887.439 ***	-13903.459 ***	-14009.758 ***
		(5117.237)		(4945.171)	(4880.967)	(4186.693)	(4181.661)	(4181.561)
field_exp21 - 30 years:genderWoman		-27971.809 ***		-29147.813 ***	-29545.621 ***	-21768.894 ***	-21679.884 ***	-21795.637 ***
		(5619.375)		(5429.326)	(5358.786)	(4596.536)	(4591.046)	(4590.930)
field_exp31 - 40 years:genderWoman		-17581.031 *		-17503.351 *	-17950.723 *	-7648.653	-7433.630	-7553.913
		(8228.457)		(7949.878)	(7846.561)	(6748.574)	(6740.577)	(6740.108)
field_exp41 years or more:genderWoman		-7106.165		-10096.647	-11137.299	337.307	-396.326	-543.267
		(17053.820)		(16478.297)	(16264.168)	(13939.868)	(13924.525)	(13923.153)
educationSome college			6664.759 *	6636.025 *	6334.711 *	5116.750 *	5004.721 *	4982.621 *
			(2996.167)	(2959.619)	(2921.192)	(2503.433)	(2500.511)	(2500.253)
educationCollege degree			20794.145 ***	20287.413 ***	19796.872 ***	18576.157 ***	18436.607 ***	18425.183 ***
			(2747.005)	(2714.021)	(2678.884)	(2303.248)	(2300.621)	(2300.366)
educationMaster's degree			23589.736 ***	23335.704 ***	23333.386 ***	28704.406 ***	28548.266 ***	28515.267 ***
			(2765.094)	(2731.568)	(2696.054)	(2327.655)	(2325.034)	(2324.834)
educationProfessional degree (MD, JD, etc.)			45943.690 ***	45707.334 ***	45647.748 ***	52250.081 ***	52182.832 ***	52132.988 ***
			(3081.052)	(3043.512)	(3003.945)	(2692.734)	(2689.748)	(2689.570)
educationPhD			36354.897 ***	36615.006 ***	36387.719 ***	45722.324 ***	45422.768 ***	45417.812 ***
			(3081.974)	(3044.832)	(3005.274)	(2632.831)	(2630.980)	(2630.682)
raceBlack				-18415.931 ***	-15219.157 ***	-10056.790 ***	-9991.410 ***	-10010.249 ***
				(2494.993)	(2469.422)	(2120.425)	(2117.969)	(2117.751)
raceOthers				-19825.444 ***	-17587.033 ***	-11492.685 ***	-11466.127 ***	-11474.295 ***
				(1862.273)	(1842.573)	(1582.357)	(1580.617)	(1580.442)
raceWhite				-23129.046 ***	-18850.259 ***	-11922.140 ***	-11797.448 ***	-11823.976 ***
				(1543.285)	(1543.007)	(1327.160)	(1325.828)	(1325.751)
pop_estimate_2019_m					496.117 ***	414.710 ***	413.930 ***	413.058 ***
					(28.559)	(24.571)	(24.546)	(24.547)
researchTRUE						-1355.889	-1207.748	-875.806
						(1799.811)	(1797.860)	(1806.191)
managerTRUE						8292.792 ***	8229.515 ***	8232.859 ***
						(719.191)	(718.516)	(718.436)
engineerTRUE						22900.445 ***	22672.079 ***	22686.156 ***
						(1090.997)	(1090.502)	(1090.403)
industryBusiness or Consulting						14160.591 ***	14381.124 ***	14444.830 ***
						(1737.439)	(1735.976)	(1736.104)
industryComputing or Tech						19739.674 ***	19520.670 ***	19519.668 ***
						(1217.430)	(1217.248)	(1217.110)
industryEducation (Higher Education)						-24655.285 ***	-24421.383 ***	-24394.782 ***
						(1321.490)	(1321.082)	(1321.006)
industryEducation (Primary/Secondary)						-27573.822 ***	-27838.305 ***	-27799.251 ***
						(1690.342)	(1690.152)	(1690.085)
industryEngineering or Manufacturing						-3540.355 *	-3336.457 *	-3256.983 *
						(1490.069)	(1488.809)	(1489.232)
industryGovernment and Public Administration						-6801.635 ***	-6551.443 ***	-6437.312 ***
						(1402.622)	(1401.703)	(1402.840)
industryHealth care						-4316.280 **	-4243.986 **	-4164.012 **
						(1354.116)	(1352.599)	(1353.105)
industryInsurance						-3274.070	-3313.004	-3312.386
						(1986.342)	(1984.418)	(1984.192)
industryLaw						-5477.892 **	-5400.347 **	-5376.811 **
						(1785.729)	(1783.907)	(1783.747)
industryMarketing, Advertising & PR						450.697	378.725	363.498
						(1561.097)	(1559.309)	(1559.152)
industryMedia & Digital						-4514.505 *	-4483.965 *	-4457.684 *
						(1775.735)	(1773.998)	(1773.850)
industryNonprofits						-15804.795 ***	-15631.462 ***	-15611.513 ***
						(1270.969)	(1269.925)	(1269.824)
industryRecruitment or HR						-2879.708	-3112.659	-3128.515
						(2063.699)	(2061.669)	(2061.451)
industryRetail						-20691.092 ***	-20791.356 ***	-20777.168 ***
						(2110.220)	(2108.144)	(2107.917)
data_relatedTRUE						7365.560 ***	7170.066 ***	5791.150 **
						(1884.875)	(1883.043)	(2018.888)
scientistTRUE						12911.077 ***	12713.710 ***	9426.006 **
						(2605.884)	(2603.049)	(3129.243)
databaseTRUE						-16577.967 *	-16550.496 *	-15181.333 *
						(6445.897)	(6438.143)	(6477.934)
librarianTRUE						-11263.970 ***	-11402.890 ***	-11437.726 ***
						(2118.660)	(2116.375)	(2116.214)
add_context_jobTRUE							-2928.628 ***	-2916.277 ***
							(623.222)	(623.185)
add_context_incTRUE							2995.721 **	2993.794 **
							(919.047)	(918.943)
data_relatedTRUE:scientistTRUE								10379.524
								(5484.449)
#observations	11366	11366	11366	11366	11366	11366	11366	11366
R squared	0.128	0.133	0.170	0.191	0.212	0.423	0.425	0.425
Adj. R Squared	0.127	0.131	0.169	0.190	0.211	0.421	0.422	0.423
Residual SE	35289.480	35207.617	34435.944	34006.685	33564.555	28743.282	28708.695	28705.422
AIC	270300.812	270255.011	269749.237	269474.075	269177.590	265673.551	265648.174	265646.577
* p < 0.001; p < 0.01; * p < 0.05.

# calculate rmse on test set of 11 models
models <- list(m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11)
rmses <- c()
i <- 0
for (model in models){
  i = i + 1
  print(paste("model",i))
  preds <- predict(model, data_test)
  rmses[i] <- RMSE(
    pred = preds,
    obs = data_test$salary
    )
  print(paste("RMSE on train data:",summary(model)$sigma))
  print(paste("RMSE on test data:", rmses[i]))
  
  SS.total      <- with(data_test,sum((salary-mean(salary))^2))
  #SS.residual   <- sum(residuals(model)^2)
  SS.regression <- sum((preds-mean(data_test$salary))^2)
  #SS.total - (SS.regression+SS.residual)
  
  print(paste("R Squared on train data", summary(model)$r.squared))     
  print(paste("R Squared on test data", SS.regression/SS.total))  # fraction of variation explained by the model
  
}

## [1] "model 1"
## [1] "RMSE on train data: 37095.4502501071"
## [1] "RMSE on test data: 36985.4136059742"
## [1] "R Squared on train data 0.0362110702473326"
## [1] "R Squared on test data 0.0373349296083914"
## [1] "model 2"
## [1] "RMSE on train data: 36898.5318250807"
## [1] "RMSE on test data: 36597.9066711955"
## [1] "R Squared on train data 0.0465841987199754"
## [1] "R Squared on test data 0.0476371751180191"
## [1] "model 3"
## [1] "RMSE on train data: 36049.8427580782"
## [1] "RMSE on test data: 35753.5340710996"
## [1] "R Squared on train data 0.089938121540009"
## [1] "R Squared on test data 0.0926641460655427"
## [1] "model 4"
## [1] "RMSE on train data: 35289.4799778895"
## [1] "RMSE on test data: 34924.6767727815"
## [1] "R Squared on train data 0.128000066311433"
## [1] "R Squared on test data 0.132199529165854"
## [1] "model 5"
## [1] "RMSE on train data: 35207.617443797"
## [1] "RMSE on test data: 34830.0983571456"
## [1] "R Squared on train data 0.132575981039106"
## [1] "R Squared on test data 0.137322501017178"
## [1] "model 6"
## [1] "RMSE on train data: 34435.9443290408"
## [1] "RMSE on test data: 34127.075354642"
## [1] "R Squared on train data 0.170037088957289"
## [1] "R Squared on test data 0.17746586804058"
## [1] "model 7"
## [1] "RMSE on train data: 34006.6853010122"
## [1] "RMSE on test data: 33893.6113771057"
## [1] "R Squared on train data 0.191312823275399"
## [1] "R Squared on test data 0.200353434956173"
## [1] "model 8"
## [1] "RMSE on train data: 33564.5551861195"
## [1] "RMSE on test data: 33554.0911706585"
## [1] "R Squared on train data 0.212273508211821"
## [1] "R Squared on test data 0.22268113081223"
## [1] "model 9"
## [1] "RMSE on train data: 28743.2816284638"
## [1] "RMSE on test data: 28711.9924589569"
## [1] "R Squared on train data 0.423390974628695"
## [1] "R Squared on test data 0.413260520145657"
## [1] "model 10"
## [1] "RMSE on train data: 28708.6953277177"
## [1] "RMSE on test data: 28676.5016877011"
## [1] "R Squared on train data 0.424879416748037"
## [1] "R Squared on test data 0.415327383057971"
## [1] "model 11"
## [1] "RMSE on train data: 28705.4215821016"
## [1] "RMSE on test data: 28649.524717651"
## [1] "R Squared on train data 0.425061378093912"
## [1] "R Squared on test data 0.415699021430563"

# for model 10, comparing to 28657.84 RMSE in training data. 
# the RMSE 29507 is not very large indicating there is not very heavy over fitting problem

Ask A Manager 2021

Group 5 MAM

2021-09-21

Data cleaning

Removing NA values

Removing outliers

Removing very small age group

Transforming into ordered `factor` datatype

Remove problematic entries

Selecting industries

Unifying currencies

Exploratory Data Analysis

Counts

Salary

Industry

Salary ,Gender and Industry

Education

Race

Count

Race and Mean Salary

Location

Changed Industry? vs salary

Statistical Tests

Gender vs Salary

General Statistics & Boxplot

T-Test

Confidence Intervals

Bootstrap Test

Gender vs Education

Race vs Salary

Race vs Education

Changed Industry? vs salary T.Test

Regression Analysis

Ask A Manager 2021

Group 5 MAM

2021-09-21

Data cleaning

Removing NA values

Removing outliers

Removing very small age group

Transforming into ordered factor datatype

Remove problematic entries

Selecting industries

Unifying currencies

Exploratory Data Analysis

Counts

Salary

Industry

Salary ,Gender and Industry

Education

Race

Count

Race and Mean Salary

Location

Changed Industry? vs salary

Statistical Tests

Gender vs Salary

General Statistics & Boxplot

T-Test

Confidence Intervals

Bootstrap Test

Gender vs Education

Race vs Salary

Race vs Education

Changed Industry? vs salary T.Test

Regression Analysis

Transforming into ordered `factor` datatype